{"paper":{"title":"On the local constancy of regularized superdeterminants along special families of differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AT","math.DS","math.MP","math.SP"],"primary_cat":"math.DG","authors_text":"Michele Schiavina, Thomas Stucker","submitted_at":"2025-05-06T10:30:43Z","abstract_excerpt":"We consider the flat-regularized determinant of families of operators of the form $D_\\tau=[\\delta_\\tau,d_\\nabla]$, where $\\tau\\to\\delta_\\tau$ are families of degree $-1$ maps in the twisted de Rham complex $\\left(\\Omega^\\bullet(M,E),d_\\nabla\\right)$ generalizing the (twisted) Hodge codifferential. We show that under suitable assumptions, both geometrical and analytical in nature, the flat-regularized determinant of $D_\\tau$, restricted to the subspace $\\mathrm{im}(\\delta_\\tau)$, is constant in $\\tau$. The general result we present implies both local constancy of the Ray--Singer torsion and of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03404","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.03404/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}